For the control enginers: how often do you use mathematics and physics in your jobs?
Yes, and no. It's not what you see in the classroom. For example, I have to know what the reactivity of certain reagents will be so that I can figure out what coatings are appropriate for a metered pump. I have to work with valves to determine where and whether there is any likelihood of steam flashing, or large pumps to determine if there is a possibility of cavitation. I also use shortcut equations for lots of things such as the Bessel Nulls for setting FM transmitter deviation, or making estimates of the poles and zeros of a PID controller to evaluate stability. I have also used signal processing methods to estimate flow in and out of irregularly shaped storage tanks.
On the other hand, if you think you'll be solving integrals or partial differential equations with pencil and paper --NO. It's not like that. The concepts are important and they're critical for evaluating whether your shortcut estimates still apply, but coming up with actual solutions to new equations is rare.
Only one more question:
Was Control Engineering your undergraduate, or you specialized in it later? Like I said, I am a student of mechanical engineering. So, where do most control engineers come from? Electrical, eletronics, mechanical?
I started off as an Electrical Engineering student. I worked during the day as an instrumentation and telecommunications technician. When I graduated, I worked a lot on early SCADA and DCS/PLC control systems. I learned a lot about all sorts of programming, from embedded programming, systems programming, applications programming, Relay Ladder Logic and so on. After that, I spread out toward process and instrumentation design.
I know other control engineers who came from Chemical Engineering, Civil Engineering, and even IT backgrounds. The formal teaching for this field is, well, very theoretical. That's not wrong, but it means that most engineers in this field have a very long flat learning curve.